STATISTICAL ANALYSIS AND MARKOV MODELING OF DYNAMIC RESOURCE PROVISIONING IN ELASTIC OPTICAL NETWORKS Adriana de Nazaré Farias da Rosa

FEDERAL UNIVERSITY OF PARÁ

INSTITUTE OF TECHNOLOGY

POST GRADUATE PROGRAM IN ELECTRICAL ENGINEERING

STATISTICAL ANALYSIS AND MARKOV

MODELING OF DYNAMIC RESOURCE

PROVISIONING IN ELASTIC OPTICAL NETWORKS

Adriana de Nazaré Farias da Rosa

TD - 08/2015

UFPA/ITEC/PPGEE Campus Universitário do Guamá

FEDERAL UNIVERSITY OF PARÁ

INSTITUTE OF TECHNOLOGY

POST GRADUATE PROGRAM IN ELECTRICAL ENGINEERING

Adriana de Nazaré Farias da Rosa

STATISTICAL ANALYSIS AND MARKOV

MODELING OF DYNAMIC RESOURCE

PROVISIONING IN ELASTIC OPTICAL NETWORKS

TD - 08/2015

UFPA/ITEC/PPGEE Campus Universitário do Guamá

FEDERAL UNIVERSITY OF PARÁ

INSTITUTE OF TECHNOLOGY

POST GRADUATE PROGRAM IN ELECTRICAL ENGINEERING

Adriana de Nazaré Farias da Rosa

STATISTICAL ANALYSIS AND MARKOV

MODELING OF DYNAMIC RESOURCE

PROVISIONING IN ELASTIC OPTICAL NETWORKS

Doctoral Thesis submitted to examining commit-tee of the Post Graduate Program in Electrical En-gineering from Federal University of Pará as a re-quirement to obtain the title of Doctor in Electrical Engineering.

UFPA/ITEC/PPGEE Campus Universitário do Guamá

Dados Internacionais de Catalogação-na-Publicação (CIP) Sistema de Bibliotecas da UFPA

Rosa, Adriana de Nazaré Farias da,

1983-Statistical analysis and markov modeling of dynamic resource provisioning in elastic optical networks / Adriana de Nazaré Farias da Rosa. - 2015.

Orientador: João Crisóstomo Weyl Albuquerque Costa;

Coorientador: Solon Venâncio de Carvalho. Tese (Doutorado) - Universidade Federal do Pará, Instituto de Tecnologia, Programa de Pós-Graduação em Engenharia Elétrica, Belém, 2015.

1. Comunicações óticas - modelos matemáticos. 2. Fibras óticas. 3. Markov, processos de. I. Título.

FEDERAL UNIVERSITY OF PARÁ INSTITUTE OF TECHNOLOGY

POST GRADUATE PROGRAM IN ELECTRICAL ENGINEERING

STATISTICAL ANALYSIS AND MARKOV MODELING OF DYNAMIC RESOURCE PROVISIONING IN ELASTIC OPTICAL NETWORKS

AUTHOR: Adriana de Nazaré Farias da Rosa

Doctoral Thesis submitted to examining committee of the Post Graduate Program in Electrical Engineering from Federal University of Pará as a requirement to obtain the title of Doctor in Electrical Engineering.

APPROVED ON 26/06/2015

THESIS EXAMINING COMMITTEE:

Prof. Dr. João Crisóstomo Weyl Albuquerque Costa

(SUPERVISOR – UFPA)

Prof. Dr. Solon Venâncio de Carvalho

(CO-SUPERVISOR – INPE)

Prof. Dr. Carlos Renato Lisboa Francês

(MEMBER – UFPA)

Prof. Dr. Maria Thereza Miranda Rocco Giraldi

(MEMBER – IME)

Prof. Dr. Maria José Pontes

(MEMBER – UFES)

Prof. Dr. Marcelo Eduardo Vieira Segatto

(MEMBER – UFES) SIGNATURE:

Prof. Dr. Evaldo Gonçaves Pelaes

(Head of the Department – PPGEE/ITEC/UFPA)

Acknowledgments

It is my pleasure to thank and acknowledge those whose direct involvement made possible the production and completion of this thesis.

I am truly grateful to my supervisors, Professor João Crisóstomo and Professor Solon Carvalho for their time, guidance and support throughout this whole process. I am very much obliged for their most valuable mentorship, advice, encouragement and friendship. All the lessons they have taught me, especially the work attitude, are very precious and for the whole life.

I would like to express my deepest gratitude to Professor Lena Wosinska for accepting me as her Ph.D exchange student and always being very supportive from the start. My technical visit to her group during my Ph.D study has been inspiring me in all these years. Without her excellent supervision, my Ph.D study would not be completed. My very special thanks are conveyed to Dr. Cicek Cavdar, who generously shared her friendship and knowledge with me, and, together with Professor Lena, introduced me to the world of Elastic Optical Networks. In addition, I would like to thank CAPES, under grant agreement n◦ _{0953/11-3, and CNPq within the project n}◦ _{870269/2000-3, under grant}

agreement 142166/2010-3, for the financial support and for providing me the opportunity to study in Sweden.

A special thank you should be given to my “LEA family” for all the happy times we shared during these years. Many thanks for providing me with a joyful environment in my daily work. My infinite gratitude and admiration goes to my closest friends, in especially to my eternal Vida, Éder Patrício. They have been an abundant source of happiness and inspiration, and motivation to persevere in the most difficult times.

Living abroad half a world from home is definitely not easy, but I am lucky enough to have found lovely friends in the other side of the ocean. Many thanks go to my “ONLab family”, in especially to my friend Mozhgan Mahloo, for the friendly and joyful relationship we have in our professional and personal lives.

Last but not least, I am forever indebted to my parents and my sister for their everlasting love and indispensable support for my whole life, which has encouraged me to pursue my personal and professional goals. I would like to express my heartfelt appreciation to my beloved Boris Dortschy, for his unconditional understanding and generous encouragement during the last moments of my Ph.D study.

Abstract

The current trends in optical fiber communications are rapidly approaching the physical capacity limit of standard optical fiber. It is becoming increasingly important to effici-ently utilize spectral resources wisely to accommodate the ever-increasing Internet traffic demand. However, the rigid and coarse ITU-T grid specifications regarding the spectrum usage restrict the granularity of bandwidth segmentation and allocation, which frequen-tly causes a mismatch between the allocated and the actual requested link bandwidth. This often leads to over provisioning, where usually more resources are provided than necessary. Recently, the concept of elastic optical networks (EONs) has been proposed in order to reduce the waste of spectra resources. In networks with such feature enabled, modulation parameters and central frequencies are not fixed as in the traditional WDM networks: the resources can be allocated with fine granularity, which can adapt to the granularity of the requested bandwidth without over provisioning. This results in more efficient usage of spectral resources.

However, elastic optical networks must satisfy dynamic connection add and drop over spectral resources that inevitable results in fragmentation of the spectrum. In EONs, spectrum fragmentation is an important and inevitable problem, because it reduces the spectral efficiency. As consequence, the blocking probability (BP) is increased due to scattered gaps in the optical grid. Currently, several metrics have been proposed in order to quantify a level of spectrum fragmentation. Approximation methods might be used for estimating average blocking probability and some fragmentation measures, but are so far unable to accurately evaluate the influence of different requested connection bandwidths and do not allow in-depth investigation of blocking events and their relation to fragmentation.

This thesis presents the analytical study of the effect of fragmentation on requests’ blocking probability.In this study, new definitions for blocking that differentiate between the reasons for the blocking events were introduced. An analytical framework based on Markov modeling was proposed in order to calculate steady-state probabilities for the different blocking events and to analyze fragmentation related problems in elastic optical links under dynamic traffic conditions. Statistical investigations were derived in order to investigate how different allocation request sizes contribute to fragmentation and blocking probability.

by system defragmentation. We also show how efficient spectrum allocation policies re-ally are in reducing the part of fragmentation that in particular leads to actual blocking events.

Simulation experiments are carried out showing good match with our analytical results for blocking probability in a small scale scenario. Simulated blocking probabilities for the different blocking events are provided for a larger scale node- and network-wise operation scenario in elastic optical networks.

List of Figures

Figure 1 – Spectrum utilization for different bit rate links . . . 16

Figure 2 – Time-frequency relation of a windowedsinc-pulse for two different rec-tangular time window widths . . . 27

Figure 3 – Possible multiplexing scheme of sinc-shaped Nyquist pulses . . . 28

Figure 4 – Time-frequency relation of an OFDM symbol showing three sub-carriers time-domain signals and their spectral relation . . . 30

Figure 5 – Three OFDM channel with three sub-carriers frequency-multiplexed to form a super-channel . . . 31

Figure 6 – Illustration of optical channel assignment for fixed and elastic grid . . . 34

Figure 7 – Network optimization for Elastic Optical Networks . . . 37

Figure 8 – Elastic resource allocation used to carry different services/applications with custom bandwidth allocation . . . 39

Figure 9 – Example of bandwidth selective WXC in the RSA . . . 41

Figure 10 – Example of spectrum fragmentation in a dynamic scenario . . . 43

Figure 11 – Example of spectrum configuration . . . 46

Figure 12 – Possible spectrum configuration resulting from FF, SF, EF and RND SA policies . . . 47

Figure 13 – Flow diagram for the Elastic SA framework . . . 55

Figure 14 – Average fragmentation . . . 65

Figure 15 – Spectrum fragmentation by request size for FF, SF, EF and RND . . . 66

Figure 16 – Total blocking probability for different SA policies . . . 66

Figure 17 – Blocking probability by request size for FF,SF,EF and RND . . . 67

Figure 18 – Fragmentation-blocking for different SA policies and link loads . . . 68

Figure 19 – Resource-blocking for different SA policies and link loads . . . 68

Figure 20 – Contrast between RND,FF, SF and EF SA strategies when resource-blocking starts dominating over fragmentation-resource-blocking . . . 69

Figure 21 – Total blocking probability for different SA policies for large scale EOL . 71 Figure 22 – Fragmentation-blocking for different SA policies and link loads for large scale EOL . . . 71

Figure 23 – Resource-blocking for different SA policies and link loads for large scale EOL . . . 72

Figure 25 – Total blocking probability for an elastic network-wise scenario as a function of the load, assuming N = 300 slots . . . 74 Figure 26 – Fragmentation-blocking and resource-blocking for an elastic

network-wise scenario, assuming N = 300 slots; contrast between RND, FF,

List of Tables

Table 1 – Comparison of fragmentation metrics resulting from different SA policies 47

Table 2 – Number of states for Random-SA policy . . . 64 Table 3 – BP of different SA policies for small scale EOL . . . 70 Table 4 – Resource- and fragmentation-blocking of different SA policies for small

scale EOL . . . 70 Table 5 – Relation of end-to-end link definition and involved nodes for a network

Acronyms

ADC Analog-to-Digital Conversion AOTF Acoustic-Optic Tuneable Filters AWG Arrayed Waveguide Gratings BP Blocking Probability

BV-OXC Bandwidth Variable Optical Cross Connect

BV-ROADM Bandwidth Variable Contentionless Reconfigurable Optical Add/Drop Multi-plexer

BV-WSS Bandwidth Variable Wavelength Selective Switch CD Chromatic Dispersion

CDC-ROADM Colorless, Directionless and Contentionless Reconfigurable Optical Add/Drop Multiplexer

CO-OFDM Coherent Optical Orthogonal Frequency Division Multiplexing CTMC Continuous Time Markov Chain

DAC Digital-to-Analog Conversion DSP Digital Signal Processing

DWDM Dense Wavelength Division Multiplexing EDFA Erbium-Doped Fiber Amplifiers

EOL Elastic Optical Link EON Elastic Optical Network FFT Fast Fourier Transform FGB Fiber Bragg Gratings FON Filterless Optical Network GBE Global Balance Equation IFFT Inverse Fast Fourier Transform ILP Integer Linear Programming IPTV Internet Protocol Television ISI Inter-Symbol Interference

ITU-T International Telecommunication Union - Telecommunication Sector

LHS Left-Hand Side

LiN bO3 Lithium Niobate

MC-OXC Multi-Granular Optical-Cross-Connect MDP Markov Decision Process

MEMS Micro-Electro-Mechanical System MIMO Multiple-Input-Multiple-Output MVP Matrix-Vector Product

N-WDM Nyquist WDM

OADM Optical Add/Drop Multiplexer

OAWG Optical Arbitrary Waveform Generation OBS Optical Burst Switching

OOK On/Off Keying

OPS Optical Packet Switching OSNR Optical Signal-Noise Ratio OXC Optical Cross Connect PLC Planar Lightwave Circuits PMD Polarization Mode Dispersion PON Passive Optical Network PSD Power Spectral Density QoT Quality of Transmission RAM Random Access Memory RHS Right-Hand Side

ROADM Reconfigurable Optical Add/Drop Multiplexer RSA Routing and Spectrum Allocation

RWA Routing and Wavelength Allocation SA Spectrum Allocation

SDM Spatial Division Multiplexing SOA Semiconductor Optical Amplifiers SOR Successive Over-Relaxation SSS Spectrum Selective Switch WBS Wavelength Band Switching WDM Wavelength Division Multiplexing WRN Wavelength Routed Network WSS Wavelength Selective Switch

Table of Contents

List of Figures . . . viii

List of Tables . . . x

Acronyms . . . xi

1 INTRODUCTION . . . 15

1.1 Motivation of the Thesis . . . 15

1.2 Challenges and Contributions . . . 17

1.3 Outline of the Thesis . . . 20

2 ELASTIC OPTICAL NETWORKING: A CLASSIFIED OVERVIEW . . . 22

2.1 Evolution of Optical Nodes and Networks . . . 22

2.2 State-of-the-Art of Optical Nodes and Networks . . . 24

2.2.1 High Capacity Transmission . . . 24

2.2.2 High Speed Channel Generation . . . 25

2.2.2.1 Nyquist WDM . . . 25

2.2.2.2 Coherent Optical Orthogonal Frequency-Division Multi-plexing (CO-OFDM) . . . 29

2.2.3 Optical Networks that Provide Dynamic Bandwidth . . . 31

2.3 Need for Elastic Spectrum Allocation . . . 32

2.4 Progress toward Elastic Spectrum Allocation . . . 33

2.5 Issues and Challenges in Elastic Optical Networking . . . 34

3 DYNAMIC RESOURCE PROVISIONING IN ELASTIC OPTICAL NET-WORKS . . . 36

3.1 Design Scope Aspects of Networking Optimization . . . 36

3.2 Dynamic Resource Provisioning in EONs: Definition and Complexity . . . 38

3.2.1 Routing and Spectrum Allocation (RSA) Problem . . . 40

3.2.2 Off-line and On-line Approaches . . . 41

3.3 Spectrum Fragmentation Problem . . . 43

3.3.1 Spectrum Allocation (SA) Policies . . . 44

3.3.2 Fragmentation Ratio Calculation . . . 44

4 ELASTIC SA FRAMEWORK BASED ON MARKOV MODELING . . . . 49

4.1 Markov Modeling . . . 49

4.1.2 Numerical Methods . . . 51

4.1.2.1 Jacobi Method . . . 53

4.1.2.2 Gauss-Seidel Method . . . 54

4.1.2.3 Successive Over-Relaxation (SOR) Method . . . 54

4.1.2.4 Sparse Equations and Least Squares (LSQR) Method . . . 54

4.2 Elastic SA Framework . . . 55

4.2.1 State-Space Generation . . . 56

4.2.2 Transition-Rate Matrix Generation and Steady-State Probabilities . 58 4.3 Calculation of Blocking Probabilities . . . 61

5 STATISTICAL ANALYSIS OF NODE- AND NETWORK-WISE OPERA-TION SCENARIO IN ELASTIC OPTICAL NETWORKS . . . 63

5.1 Performance Results of Node-Wise Modeling . . . 63

5.1.1 Spectrum Fragmentation Analysis . . . 65

5.1.2 Blocking Probability Analysis . . . 66

5.1.3 Resource- and Fragmentation-Blocking Analysis . . . 67

5.2 Monte Carlo Simulation . . . 69

5.3 Performance Results of Network-Wise Modeling . . . 72

5.3.1 Description of the Network . . . 72

5.3.2 Description of the Simulation . . . 72

5.3.3 Results . . . 74

6 CONCLUSIONS AND FUTURE WORKS . . . 77

6.1 Conclusion . . . 77

6.2 Future Research . . . 78

Bibliography . . . 81

1 INTRODUCTION

1.1

Motivation of the Thesis

A tremendous growth of Internet traffic volume has been observed in the last few years, mainly due to an increased number of Internet users along with a massive deployment of broadband access networks and the development of new bandwidth demanding Inter-net applications. With the latest advances in web-based applications available for both business and residential users such as e-services, Internet Protocol television (IPTV), video on demand, cloud and grid computing applications as well as emerging social net-works demonstrate unpredictable changes in bandwidth and geographical traffic patterns. Furthermore, low price of mobile services, making it possible to access online applications anywhere and at any time, are also driving the enormous increment and variability of today’s demand.

In the near future, Global Internet traffic is expected to continue the increase at a compound annual rate of 34% [1]. As a result of this rapid increase in traffic demands, large-capacity and cost-effective optical fiber transmission systems are required for reali-zing future optical networks. So far, Wavelength Division Multiplexing (WDM) systems with up to 40 Gb/s capacity per channel have been deployed in backbone networks, while 100 Gb/s interface are now commercially available and 100 Gb/s deployment are expected soon. Moreover, it is foreseen that optical networks will be required to support Tb/s class transmission in the near future. However, scaling to this growth is challenging for conven-tional optical transmission technology as it suffers from electrical bandwidth bottleneck limitation, and the physical impairments become more severe as the transmission speed increases [2].

On the other hand, the emerging Internet applications call for a more data-rate fle-xible, agile, reconfigurable, and resource-efficient optical network, while the fixed and coarse granularity of current WDM technology will restrict the optical network to limited bandwidth provisioning, inefficient capacity utilization, and high cost.

The need for cost and energy efficiency as well as scalability requires a flexible network that would have a fine granularity so as to adaptively provide the required capacity to sub- or super-wavelength demands. Approaches such as optical burst switching (OBS) and optical packet switching (OPS) that meet these requirements can only be viewed as long-term solutions since their enabling technologies are not yet mature [3].

an optical channel each bandwidth variable optical cross connect (BV-OXC) is able to allocate requested spectrum with fine granularity, which allows for efficient spectrum uti-lization, in contrast to fixed-grid WDM networks.

Recent advances in multi-carrier solutions such as coherent optical orthogonal fre-quency division multiplexing (CO-OFDM) [5], Nyquist WDM (N-WDM) [6] as well as optical arbitrary waveform generation (OAWG) [7] have set the stage for envisioning fully elastic optical networks. These technologies enable the formation of spectrum-efficient

super-channels, which consists of several densely packed sub-channel; the optical spec-trum is considered to be sliced into a number of frequency slots, with an appropriate width, in order to simplify the network design and modeling [8]. Therefore, offering tuna-ble bit rate from few tens of gigabits per second to terabits per second range. According to the ongoing standardization efforts in ITU-T, the minimum frequency slot unit that can be currently assigned is 12.5 GHz [9]. However, in the future the granularity can be scaled down to 6.25 GHz or below [10].

100 Gb/s-based transmission systems have been commercialized in the recent two years [11]. Since they are compatible with the 50 GHz ITU grid already deployed, the need for replacing the grid did not arise yet. Both the telecom and datacom industries are now considering data rates beyond 100 Gb/s, and 400 Gb/s is receiving a lot of attention as a possible next step. Unfortunately, the spectral width occupied by 400 Gb/s using reasonable modulation formats is too wide to fit in the 50 GHz ITU-T grid, and forcing it to fit by adopting a higher spectral efficiency modulation format would only allow short transmission distances [11]. Figure 1 shows a comparison of an existing ITU-T grid and an elastic optical grid. As one can see, the fixed grid is not able to support bit rates of 400 Gb/s and 1 Tb/s at standard modulation formats, as they overlap with at least one 50 GHz grid boundary [12].

Figure 1: Spectrum utilization for different bit rate links [12].

1.2

Challenges and Contributions

Although elastic optical networks present some similarities to wavelength routed WDM networks, the flexible properties of EONs raise new challenges from the network plan-ning and resource provisioplan-ning point of view; in EONs, the allocated spectrum is adap-ted according to the requesadap-ted bit rate, transmission distance, and modulation format. Furthermore, the evolution of resource units from an entire wavelength to a frequency slot leads to fundamentally new constraints in spectrum allocation practices, such as e.g.,

spectrum contiguity. Instead of one wavelength, a connection is now assigned one or se-veral frequency slots, depending on whether the capacity requirement of a connection is larger than the capacity of one slot unit. If multiple slots are required, they have to be contiguous, i.e., a connection request can only be satisfied if a sufficient number of free and adjacent slots is available.

The fundamental problem in elastic optical networks is to route and to assign the spectrum resources to accommodate the traffic demands, which is defined as the routing and spectrum allocation (RSA) problem [4]. In the literature, many studies have been conducted during the last three years in order to address the RSA problem [13–17]. The RSA problem in EONs is analogous to the conventional routing and wavelength allocation (RWA) concept in wavelength routed WDM networks. However, due to the new properties of EONs, RWA algorithms cannot be directly applied.

The RSA problem can be divided into two stages for a simpler (suboptimal) solution. As mentioned before, many works have investigated the possible advantages of using a flexible spectrum allocation (SA) concept. Static SA problem is considered for the network design or planning phase [14, 18] where the objective is to minimize the number of necessary frequency slots while provisioning the given traffic demand. Dynamic SA problem, on the other hand, is applied during the network operation, when new lightpaths requests should be served upon arrival [19–21]. Under these conditions, the heterogeneous bandwidth allocation may result in fragmentation of the spectral resources.

regeneration at selectively placed regenerators. In [26], a QoT-aware RSA algorithm has been proposed, which allocates the modulation level and spectrum by estimating the QoT of the network via a closed-form expression for physical layer impairments.

The statistical analysis of dynamic spectrum allocation was introduced only recently. Blocking probability, resource utilization as well as spectrum fragmentation are the com-mon metrics of performance in EONs, which can be used to dimension network and link capacities while taking into account the dynamics of lightpath requests [8]. It is important to note that the methods utilized to analyze traditional WDM networks are not applicable to assess the performance of EONs. In [27], the authors proposed a birth-death model to analyze the blocking performance for three different spectrum allocation policies, under time-varying traffic in EONs. Although, by applying some relaxation assumptions, the dynamic SA problem is transformed into a static one. In [28], the authors presented an iterative procedure in order to estimate the blocking probability in EONs, with and without spectrum conversion, by approximating the bandwidth utilization ratio. In [8], the authors presented a continuous time Markov chain to calculate spectrum fragmen-tation and average blocking probability as well as resource utilization of a stand-alone EON link, considering First-Fit (FF) and Random-Fit (RND) SA approaches. In [29], Beyranvand et. al. presented the first attempt for performance evaluation of node- and network-wise operation scenarios in EONs. They developed an analytical framework and investigated average blocking performance and spectrum fragmentation, in scenarios with and without spectrum conversion, considering FF and RND as spectrum allocation po-licies. The performance of the framework was compared to exact results for up to eight slots. The authors also show how elastic optical network performance modeling can be broken down to link modeling, in order to significantly reduce the complexity. Recently, in [30] the effect of spectrum fragmentation on the blocking probability of EONs under simplified model of EON operation was investigated with certain fragmentation and uti-lization. However, due to the high complexity of the model performance, evaluation was only possible by using simulations.

In our study we noticed that the analysis of fragmentation is not sufficient to conclude on the network performance in terms of average BP. The majority of work available in literature tends to assume that blocking probability for future requests should increase monotonically with increasing spectrum fragmentation [20, 31]. Based on this, previous studies have tried to quantify the level of spectrum fragmentation by proposing vari-ous fragmentation formulas [31–34]. To the best of our knowledge, none of the previvari-ous works on statistical analysis of dynamic spectrum provisioning in the literature considers and investigates the reasons for blocking events, but rather the overall average blocking probability of the system. However, blocking can occur not only because of spectrum fragmentation, but in general due to lack of available resources to serve connection re-quests. It is usually not considered to which extent and why spectrum allocation policies

proactively minimize the number of blocking events.

In this thesis, we study the spectrum assignment problem in elastic optical networks independently from the routing. Our goal is to provide a mathematical Markov-based model to analyze the statistical performance of elastic optical links for on-line or dynamic traffic conditions. In this respect, the analytical study of the effect of fragmentation on requests blocking probability is presented. The real merits of flexible bandwidth allocation for elastic optical links in terms of wasted (unusable) free spectrum, which is defined as fragmentation, is discussed. Note that fragmentation problem in elastic optical networks is very similar to external memory fragmentation in computer science, so that we borrow some measures and tools from this field in order to quantify fragmentation in elastic optical links.

The major contributions of this work are:

• We formally define the spectrum allocation (SA) problem, taking into account the fragmentation issue. In addition to that, we first present an analytical model to analyze and quantify the blocking probability and fragmentation in an elastic opti-cal link (frequency grid) [35]. Moreover, we compare three existing and one proposed dynamic spectrum allocation schemes by using our framework and discuss the rela-tion of fragmentarela-tion and blocking probability [35];

• We also introduce new definitions for blocking that differentiate between the re-asons for the blocking events [36]. Furthermore, we introduce an accommodated fragmentation metric from the field of dynamic memory allocation research that allows differentiating between very small variations of spectrum occupancy, which can depend on different spectrum allocation strategies [36]. Based on these new measures, we investigate how various request sizes contribute to fragmentation and blocking probability;

• Moreover, we show to which extend blocking events, due to the fact of insufficient amount of resources, become inevitable and compare to the amount of blocking events due to fragmented spectrum. Based on this comparison, we draw conclusions on the possible gains one can achieve by system defragmentation. We also reveal how efficient dynamic spectrum allocation schemes really are in reducing the part of fragmentation that effectively leads to actual blocking events.

• Finally, we developed a Monte Carlo simulation in order to provide expected results for large scale elastic node- and network-wise operation scenarios for all types of blocking events. Therefore, we show that small scale analytical results can allow drawing conclusions on larger scale elastic grids.

Moreover, the model can be easily adopted to evaluate networks based on broadcast-and-select architecture, i.e., without any switching nodes between the source and destination. Examples of such architecture are passive optical network (PON) in the access segment and so called filterless optical network (FON) in the core segment where active switching nodes are replaced by passive splitters/combiners. While different types of PONs are standardized and widely deployed in the fiber access networks, FONs concept has been recently proposed [37] as a cost-effective, energy-efficient and reliable alternative to the active optical switched core networks. The passive gridless architecture of FONs makes them naturally suitable for elastic optical networking without the need to replace the switching and filtering devices at nodes. Thanks to the above advantages, we expect that the filterless architecture will gain interest of the network providers in the future optical core and submarine network deployments and we believe that our elastic optical link model will be very useful for analysis of the network-wide performance of elastic FONs.

1.3

Outline of the Thesis

The work included in this thesis addresses important aspects of the resource provisio-ning paradigm in elastic optical networking, i.e., the performance of dynamic spectrum allocation schemes, spectrum fragmentation, and the effect of fragmentation on requests blocking probability. It is based on research papers published as international contri-butions in the area of next generation of optical networks. This thesis is organized as follows.

Chapter 2 starts with a summary of the evolution of optical nodes and networks emphasizing the increased flexibility added with each evolutionary stage. It then presents state-of-the-art optical systems scalable to Tb/s, high-capacity transmission experiments and optical systems that provide dynamic bandwidth. The requirements for creating optical networks with such state-of-the-art systems and technology are discussed, leading to the conclusion that there is a need for higher flexibility in the allocation of spectral resources and the flexibility of optical nodes to use functional modules only where required. Ongoing evolution towards elastic spectrum allocation along with several issues brought about by this new paradigm are also presented.

Chapter 3 introduces the concept of elastic allocation of spectral resources, focusing most in dynamic spectrum provisioning and its main matters related to the network level. It then provides an overview of the routing and spectrum assignment (RSA) problem, and discusses one of the key issues in design and optimization of elastic optical networking under dynamic traffic conditions, the so called spectrum fragmentation problem. After that, we introduce four spectrum allocation schemes including a genuine one, presented in our conference contribution [35]. With in this contribution, we also introduced for the first time, to the best of our knowledge, an analytical modeling approach for flexible spectrum

allocation under dynamic traffic conditions in the literature. Finally, the fragmentation metrics considered in this thesis are provided, and their ability to reflect the spectrum occupancy is discussed.

Chapter 4, along with chapters 3 and 5, presents the main contributions of this thesis. It first shows the overall process of Markov modeling of real-life systems with inherently stochastic behavior. We then explain the methodology used to evaluate the performance of the model presented in this thesis, including a review of some principal alternatives to efficiently compute the steady-state probabilities. Then, the Markov-based framework, presented in our journal contribution [36], is introduced. For the last, we propose new classifications for blocking events that we use in the following to statistically analyze the performance of different SA schemes.

The performance results follow in Chapter 5. After computing the steady-state pro-babilities of the spectrum usage in an elastic optical link, spectrum fragmentation and blocking probability are statistically evaluated. After that, the analytical results are bac-ked up by results from a Monte Carlo simulation. The results aforementioned have been reported in [36]. Finally, the new definitions of blocking events are applied in the analysis of the dynamic resource provisioning in an elastic optical network scenario.

2 ELASTIC OPTICAL NETWORKING: A

CLASSIFIED OVERVIEW

The evolution of optical nodes and networks has been characterized by continuous enhan-cements in capacity, reach, functionality, resiliency, etc. Moreover, such enhanenhan-cements have inherently meant increasing flexibility. This chapter discusses the evolution of opti-cal nodes and networks and shows how flexibility has been continuously increasing with each evolutionary stage. It also presents state-of-the-art of optical systems that provide high channel and total transmission capacity and discusses their networking requirements. Thus, it shows that there is the need to further increase flexibility in the allocation of spectral resources and the flexibility of optical nodes so that they are able to efficiently support on-demand services and functionality.

2.1

Evolution of Optical Nodes and Networks

Early optical technology was used mainly for point-to-point data transmission, while the processing and networking operation were done in electronics. However, the potential of optical networking to lower costs and increase performance was quickly recognized. One of the first systems proposed for optical networking was based on a passive 8x8 star coupler to broadcast signals from any input port to all output ports [38]. However, the passive star coupler introduced excessive loss, which limited the scalability of the solution.

The advent of WDM introduced additional capacity and flexibility to optical commu-nication systems. Whereas before only a single channel was carried in an optical fiber, now it was possible to transmit data using a number of wavelengths over the same fiber. Two principle pieces of new technology were required for this concept to work on a WDM link: namely optical amplifiers, colored laser sources and multiplexing/demultiplexing devices. For WDM distribution networks, however, additional technology was required. It was necessary to amplify optical signals at intermediate points to compensate for the attenuation introduced by the optical fiber and switching devices. Moreover, a way to add/drop individual wavelengths at intermediate points was needful.

OADMs to add/drop wavelengths at each node. Nevertheless, it was now possible to connect one node to various other nodes using the same fiber by selecting different trans-mission wavelengths for different connections. Hence, ring network topologies were also more flexible than early point-to-point systems.

Although OADMs were widely used for the deployment of ring networks, a different type of optical node was required to implement mesh networks. Thus, in the 1990s several optical cross connect (OXC) [38] designs were developed with the intention of performing the switching function directly in the optical domain, thereby avoiding the use of ex-pensive electronic switching at intermediate nodes. OXCs were first implemented using optical filters and star couplers to construct the switching matrix. Other designs used Lithium-Niobate (LiN bO3) devices or semiconductor optical amplifiers (SOA) as

swit-ching gates. In the early 2000s, the micro-electro-mechanical system (MEMS) switches were introduced, providing lower insertion loss and better scalability [39].

However, even OXCs were considered as a feasible solution for small scale systems, the size of optical networks had dramatically grown from the early systems. Optical nodes were required to switch large numbers of wavelengths, e.g., 80 wavelengths in the C-band, from several fibers [39]. Thus, 2D-MEMS switching technology, which scales up to a maximum of around 32 ports, became a bottleneck. This motivated the development of the multi-granular optical cross connect (MC-OXC). MC-OXCs aim to reduce cost and complexity of OXCs by grouping wavelengths together into bands and switching them using single cross connections.

of spectral resources.

In addition to the obvious advances in capacity and performance, it is clear that with each progressive stage of evolution additional flexibility was introduced, e.g., the introduction of wavelength granularity, the ability to add/drop individual wavelengths, reconfigurability, the increase in number of node degrees, colorless, contentionless and directionless operation and bandwidth variability.

Other types of functionality may also add flexibility to the system, e.g., wavelength, conversion, regeneration, etc. However, in ROADM architectures it is difficult to introduce additional functionality for the through-traffic due to the fact that several wavelengths are simultaneously switched over the same port. On the contrary, OXCs support additional functionality more naturally as wavelengths are split and switched individually. Thus, modules with the required functionality to operate on individual wavelengths can be positioned in the right place within the OXC. However, the requirement for a particular signal processing function is often uncertain, e.g., it may be required for some wavelengths at some time period and for other wavelengths at a different time period. Therefore, modules that provide a per-channel functionality are generally deployed for all wavelengths as there is no possibility of sharing them among several optical paths inside the OXC. A better solution would enable modules to be shared, thus improving modules’ utilization and reducing the amount of modules required to satisfy a given demand for the offered functionality, i.e., better hardware utilization and efficiency.

2.2

State-of-the-Art of Optical Nodes and Networks

Current commercial networks are still semi-static as wavelengths are established and left operational for long periods of time. They are also based on the ITU-T grid and implement some kind of ROADM or OXC technology in order to switch wavelengths across the network. In terms of optical network research and experiments, the focus is now on providing high transmission capacity per channel (beyond 100 Gb/s), bandwidth variable transmission, and high total transmission capacity towards Tb/s. This section will review some of the optical channel generation techniques scalable to Tb/s and some of the latest experimental results in this area. Then, it will present bandwidth variable systems and discuss some of the techniques used to achieve bitrate tunability. Next, it will look into the requirements for networking at such high speed and bandwidth variable channels in terms of dynamic resource allocation.

2.2.1 High Capacity Transmission

There are several techniques used or foreseen to extend total capacity, such as increasing the number of channels per fiber, transmitting higher bitrate per channel and using spatial division multiplexing (SDM) in multi-core fibers. In order to accommodate more channels

in a single fiber some experiments make use of the combined spectrum of the C- and L-band [41–47].

Also, multilevel modulation and polarization multiplexing are often used for increasing channel bitrates. For instance, polarization division multiplexing 128-QAM has been reported [42], which yielded a spectral efficiency of 11 bit/s/Hz. Also, SDM has been evolving to support higher numbers of fiber-modes or fiber cores, thereby providing higher transmission capacity. However, SDM also requires complex systems in order to operate and to be compatible with existing infrastructure, e.g., SDM (de-)multiplexers, MIMO processing [48], SDM optical amplifiers [49–51]. In addition to that, a future optical network with SDM transmission, carrying high speed and possibly also legacy channels, would require dynamic, flexible and scalable optical infrastructure.

2.2.2 High Speed Channel Generation

As traffic growth drives the demand for increasingly higher interface rates, research is conducted targeting channels in the terabit per second range. Due to technological li-mitations, such as the maximum sampling rate of analog-to-digital and digital-to-analog converters (ADC/DAC), approaches that split up the targeted data rate into multiple parallel lower data rate streams have emerged. This leads us to the concept of super-channels composed of multiple sub-channels (sub-carriers). There are different appro-aches that enable the sub-carriers to be efficiently aggregated, such as coherent optical orthogonal frequency division multiplexing (CO-OFDM), Nyquist-WDM (N-WDM) and dynamic optical arbitrary waveform generation (OAWG). In general words, optical OFDM uses orthogonal sub-carriers with spacing equal to multiples of the inverse of the OFDM symbol period [5]. N-WDM uses optical sub-carriers with almost rectangular frequency spectrum closer or equal to the Nyquist limit for intersymbol-interference-free transmis-sion. These sub-carriers are multiplexed with spacing closer or equal to the symbol rate with limited inter-sub-carrier crosstalk [6]. The ultimate spectral efficiency is almost identical for both methods under idealized conditions [6]. Finally, OAWG is capable of creating high-bandwidth data waveforms in any modulation format using the parallel synthesis of multiple coherent spectral slices [7].

2.2.2.1 Nyquist WDM

Above 10 Gb/s, transmission impairments, mainly chromatic dispersion (CD) [38] and polarization mode dispersion (PMD) [38], increase drastically and limit reach and transmission rate. In addition, low-complexity low-cost modulation formats, such as On/Off Keying (OOK), are difficult to realize at high speed, since they require extremely high speed ADCs and digital signal procession (DSP). A way out is to separate the available spectrum in simple channels with a modulation format that allows for small

guardbands, corresponding to small channels gaps in DWDM.

A required channel gap depends on the decay of sidelobes, out-of-band leakage in real modulation of signals, distortion and windowing effects on transmission impulses. For a maximum packing of simple channels in frequency domain, each channel would (completely) occupy available bandwidth, thus having a rectangular spectrum. Extremely sharp filters would allow to separate the channels and process them individually. Optical filters with a transition bandwidth of approximately only 10% of the pass-bandwidth have been demonstrated in [52].

At the same, the Nyquist-Shannon sampling theorem [53, 54] states that in order not to have inter-symbol interference (ISI) after sampling (A/D conversion), each channel’s pulse shape should be such that its periodic extension (by the sampling rate) in frequency-domain does not overlap with the original continuous time signal’s spectrum. Both requi-rements, dense allocation of channels and low ISI after windowing and filtering effects can be achieved with Nyquist-pulses withsinc function characteristics. They possess a (near) rectangular spectrum, enabling data to be encoded in a minimum spectral bandwidth and satisfying by essence the Nyquist criterion of zero ISI. This property makes them very attractive for communication systems, since data transmission rates can be maximized while the spectral bandwidth usage is minimized using only minimal guardbands [55].

The sinc function is defined as:

sinc(x) = sin(x)

x (2.1)

and extends infinitely on the positive and negative time-axis. For convenience we define

rect(x) =

 



1; |x|<0.5

0; otherwise (2.2)

A perfect rectangular impulse in time domain results in an infinitely wide occupied spectrum due to the relation of symbol length vs. channel spectrum, as

rect

t T

❞ t T ·sinc (πT f), (2.3)

one of the technical reasons for having generous channel spacing in fixgrid WDM in order not to distort used high-speed transmission pulses due to filtering effects of, e.g., arrayed

Figure 2: Time-frequency relation of a windowed sinc_{-pulse for two different rectangular time window}

widths: (a)T = 4_{/F with its PSD in (b); and (c)T} = 16_{/F with its PSD in (d) –T andF as}

in (2.3) and (2.4).

waveguide grating (AWG), if symbol timeT gets extremely short, and introduce crosstalk. Fourier theory also tells us, at the same time, the symmetry relation

sinc(πF t) ❞ t 1

F ·rect

f F

. (2.4)

A signal with a perfectly rectangular spectrum requires generating time-domain im-pulses ranging from -∞ to +∞ in time, which is not achievable due to the causality requirement in real world. Windowing techniques are applied to each pulse in order to limit its temporal extend and control the roll-off and spectral sharpness in frequency-domain.

Figure 2 illustrates the effect of time-windowing a sinc-pulse (in Fig. 2 (a) and (c)) and the resulting spectrum (in Fig. 2 (b) and (d)). The PSD of a (rectangular) windowed

sinc-pulse of temporal expandk·T, withT its main-pulse width, can be described as

PSD(f) =

kT sinc πkT ·f⊗rect T ·f

2

(2.5)

Figure 3: Possible multiplexing scheme ofsinc_{-shaped Nyquist pulses (adapted from [55]).}

However, as can be deducted from (2.3), the wider the window, the more confined becomes the left-hand term in the convolution in (2.4). In the limit, i.e. assuming an infinitely wide window (k→ ∞), the left-hand term would resemble a Dirac-pulse, thus not causing any distortion or spectrum widening. The decay and magnitude of sidelobes, as visible in the two spectra in Fig. 2, depends only on the window shape, and can be controlled by using other window types than rectangular. The width of the (near) rectangular spectrum is set by the sinc-pulse width T that also controls the repetition rate in ISI-free N-WDM transmission. Considering the transmitter is flexible and using sufficiently long transmit pulse approximations in time-domain, a transmitter can adjust the pulse transmission rates and utilize available spectrum very efficiently, requiring very reduced guardbands.

A schemes for generating modulatedsinc-pulse trains is illustrated in Fig. 3, where we assume, for the sake of simplicity a rectangular window. As in [55], a sinc-pulse train of rate 1/(T ×N)is split and fed parallel intoN n×T-delay elements with n= 0. . . N. An information sequence, after serial-to-parallel conversion (not shown), individually modu-lates each branch’s pulse. The output pulses, now each consecutively delayed by T, are combined or time-multiplexed to form a sinc-pulse train of rate 1/T and transmitted at high speed. Increasing the number of branches, without increasing incoming pulse rates, allows considering the processing of longer and longer pulses, thus shaping the effective transmit signal spectrum more and more rectangular.

At the receiver side, the high-rate pulse train is split or de-multiplexed by a factor ofN

to formN pulse trains that can be individually demodulated on lower rate1/(T×N)again. After parallel-to-serial conversion, the original information sequence can be reconstructed. Fulfilling the Nyquist-ISI criterion, thesinc-shape of each individual pulse guarantees that

neighboring pulses do almost not interfere with each other even without wide temporal separation.

Instead of time-delaying a common impulse, using a look-up table large enough to ac-commodate all possible modulated pulse configuration and their overlap and fast proces-sing in a field-programmable gate array (FPGA) or application-specific integrated circuit (ASIC) can be an all-digital alternative, if ADC can be fast enough.

2.2.2.2 Coherent Optical Orthogonal Frequency-Division Multiplexing (CO-OFDM)

As Nyquist-WDM, coherent optical orthogonal frequency division multiplexing (CO-OFDM) has been recently proposed in response to new challenges in high-speed transmis-sion link for the optical networks. OFDM is a multi-carrier transmistransmis-sion technique where a data stream is simultaneously transmitted over many individually modulated lower-rate sub-carrier tones [2] during the duration of one OFDM symbol. As will be explained, in OFDM, sub-carriers possess an orthogonality property that allows separating the infor-mation stream on each sub-carrier after proper demodulation. CO-OFDM combines the advantages of coherent transmission and detection and OFDM modulation and posses many merits that are critical for future high-speed fiber transmission systems, such as chromatic dispersion and polarization mode dispersion of the transmission system, which can be effectively estimated and mitigated.

In standard multi-carrier modulation, each sub-carrier is demodulated by means of matched filters or correlator principles. Let

s(t) = rect

t−T /2

T

·

N_Xsc−1

k=0

ckexp(j2πfkt) (2.6)

be one arbitrary multi-carrier modulation symbol, whereas Nsc denotes the number of

sub-carriers, T is the OFDM symbol time, ck would denote the information/modulation

symbol and fk the carrier frequency of the k-th sub-carrier. The rect-function is as

defined in (2.2). The matched-filter for demodulation of the k-th sub-carriers (neglecting any channel distortion or delay) would be the conjugate of the sub-carrier pulse

mk(t) = rect

t−T /2

T

·exp(−j2πfkt) (2.7)

In OFDM, the sub-carrier spacing, i.e. their relative location in frequency-domain, is in multiples of the inverse of the OFDM symbol time T. That is, the distance between any pair of sub-carrier frequencies fulfills

∆fij =fi−fj =m 1

T (2.8)

Applying matched filtering for sub-channel i to such set of sub-carriers results in

∞

R

−∞

mi(t)s(t) =

N_Psc−1

k=0

ck· T

R

0

exp(j2π∆fkit)

= T

N_Psc−1

k=0

ck·exp(jπ∆fkiT)·sinc(π∆fkiT)

(2.9)

Figure 4: Time-frequency relation of an OFDM symbol showing (a) three sub-carriers time-domain signals and (b) their spectral relation.

Because of (2.8), we have

exp(jπ∆fkiT)·sinc(π∆fikT) =

  

1; i=k

0; i6=k (2.10)

That is, different sub-carrier are orthogonal to each other. The information symbol ci of

sub-carrierican be retrieved in (2.9), even without any ISI. This is a major advantage over conventional multi-carrier modulation system with arbitrary sub-carrier spacing, since instead of using filters and requiring significant spacing between sub-carriers, OFDM mitigates inter-carrier interference by proper sub-carrier frequency choice.

Figure 4 shows three sub-carrier signal with frequencies f1 = 1/T, f2 = 2/T, f3 =

3/T. As can be seen, within the OFDM symbol period, all sinusoidal carrier pulses have complete their periods. Their spectra are identical copies of each other, but shifted by multiples of 1/T – 1/T and 2/T in this case. The spectral shape is determined by the pulse’s windowing function. In Fig. 4, the window is assumed rectangular, resulting in

sinc-function shape, see also relation (2.3).

The signal processing for sub-carrier generation and modulation in the OFDM trans-mitter can take advantage of the Inverse Fast Fourier Transform (IFFT). Demodulation in the receiver, equivalent to (2.9) can be implemented as Fast Fourier Transform (FFT). Both FFT and IFFT algorithm have efficient implementations in form of the DFT and IDFT in DSP, if Nsc is a power of 2.

Using direct up- and direct coherent down-conversion, the electrical bandwidth re-quirement can be greatly reduced for the CO-OFDM transceiver, which is extremely attractive for the high-speed circuit design, where electrical signal bandwidth dictates the cost.

For high speed channel generation, OFDM channels can be optically multiplexed

Figure 5: Three OFDM channel with three sub-carriers frequency-multiplexed to form a super-channel.

gether into asuper-channel, transporting a multiple of the capacity of an individual OFDM channel. This is illustrated in Fig. 5 for a super-channel comprising three OFDM channels with three sub-carriers each. The data stream is first divided into several channels using layer-2 link aggregation, and then OFDM modulated onto optical carriers without or at least minimumguardbands in between [2]. In Fig. 5, a guardband of one carrier-spacing is assumed, but would not be necessary in this specific case. The optical carrier frequencies need to be on a grid that preserves orthogonality in between the individual OFDM chan-nels. Carrier drift can be reduced or eliminated by locking all involved optical sources to a common optical comb. This optically aggregated super-wavelength path occupies less spectral resources than the corresponding WDM multiplexing method, thereby leaving room for additional traffic.

2.2.3 Optical Networks that Provide Dynamic Bandwidth

may be useful in the case of failure, maintenance, etc. It also makes it possible to im-prove spectral efficiency, as requested/allocated bitrates can be matched more closely and efficient modulation formats can be used for particular lightpath conditions, e.g. for long reach connections more efficient modulation formats, such as 64-QAM, are employed. In a network with mixed line rates, dynamic bitrate and modulation format transceivers could provide redundancy for several fixed transceivers, e.g. 10 Gb/s, 40 Gb/s, 100 Gb/s. Thus, fewer redundant modules would be required, which enhances cost efficiency [57].

A key enabler of dynamic bandwidth provisioning is the advent of bandwidth variable transceivers, which can adapt their bitrate and modulation format according to require-ments. Bitrate tunability can be achieved by adapting the number of optical sub-carriers that make up the high speed carrier channel [56]. Also, single-carrier and multi-carrier systems may adjust modulation formats in order to increase or decrease the number of bits per symbol. Modulation format adaptation by monitoring channel performance and using an automated control plane has been recently demonstrated [22], with alter-nation between 8-PSK, QPSK and BPSK. Although packing more bits per symbol could provide higher transmission capacity, it also requires higher optical signal-to-noise ratio (OSNR). Therefore, when a particular channel OSNR worsens the control plane triggers a modulation format change to a more robust scheme, which will also usually require more spectrum. On the contrary, when the channel OSNR improves the control plane switches the modulation format back to one that is more efficient and requires less spectrum. Thus, in order to make an efficient use of spectral resources it is necessary to dynamically adapt the allocated bandwidth according to its fluctuating channel requirements.

2.3

Need for Elastic Spectrum Allocation

The dramatic growth of Internet traffic is widely recognized by operators and market analysts alike. This trend is likely to continue due to the emergence of disruptive, bandwidth hungry applications and the proliferation of fiber to the premises and other me-ans of high bandwidth access. In order to keep up with this tremendous growth, operators will need to upgrade their network infrastructure. Currently, the most straightforward and economical way in which this can be done is to deploy additional 10G wavelengths. Thus, new 10G wavelengths are placed 50 GHz or 100 GHz away from other channels, according to the standard ITU WDM grid, until the available bandwidth is exhausted. However, the maximum capacity that can thus be provided is 800 Gb/s (i.e. 80x10G using only the C-band), which is already insufficient for heavily used backbone network links [11]. Furthermore, providing additional capacity in this manner is highly inefficient in terms of the spectral resources that are consumed.

The immediate solution to this problem is to deploy 100G links, despite their higher cost compared to 10x10G. 100G is more spectrally efficient than 10G as it can still fit

in a 50 GHz channel bandwidth, thanks to the use of DP-QPSK modulation, coherent detection, extensive use of forward error correction and electronic impairment mitigation. However, this solution is expected to be viable only for a limited time, while the Internet traffic growth is leading to a strong requirement for 400 Gb/s and 1 Tb/s in the long term. In addition to that, bitrates beyond 100G are unlikely to fit in a 50 GHz channel as that would require more complex multilevel modulation formats with higher OSNR requirements and consequently shorter reach.

Experimental demonstrations of optical transmission systems scalable to Tb/s have required more bandwidth than that provided by a single DWDM channel and, in some cases, not even multiples of 50 GHz. These channels are not supported by current optical network infrastructure designed to conform to the standard 50 GHz or 100 GHz grid. For example, OXCs and ROADMs allocate only discrete 50 GHz slots of bandwidth due to their internal WDM (de-)multiplexers. Channels that require wider bandwidths are severely distorted, if passed through such devices. Therefore, in order to efficiently support high speed channels flexible bandwidth infrastructure is required.

Elastic spectrum allocation can also increase efficiency when transporting legacy chan-nels. For example, 10G channels can be deployed with a 25 GHz channel spacing, thereby doubling spectral efficiency [60]. Narrower channel spacings may be used for lower channel bit rates, e.g., 12.5 GHz for 2.5 Gb/s [61]. Another advantage is the support for bandwidth variable transceivers, which can provide dynamic bandwidth, achieve cost reductions as fewer single type transceivers may be required, and trade-off reach and spectrum usage. For example, consider a transmitter that needs to switch from 8-PSK to QPSK in order to increase reach or maintain connectivity. In order to maintain the original bitrate, the new QPSK channel will require additional bandwidth as it is less spectrally efficient than 8 PSK. In this way, elastic spectrum allocation can be used to adjust allocated bandwidths according to channels’ requirements.

2.4

Progress toward Elastic Spectrum Allocation

The first demonstration of an elastic optical network, based on OFDM transmission, was presented in [62]. Since then, a number of studies have investigated elastic networking showing significant gains in network mean traffic [63], required spectral resources [56], capacity [59] and cost [57]. Also, several demonstrations of multi-bitrate transmission over long distances show that it is feasible for multi-Tb/s and lower speed channels to coexist in the same link using flexible spectrum allocation [64]. In the last two years, there have been important results showing the feasibility of automated adaptive transmission [65] and networking [66]. Other works have developed aspects such as translucent elastic regeneration [62] and dynamic failure restoration [67] for elastic optical networks.

Figure 6: Illustration of optical channel assignment for (a) fixed and (b) elastic grid (adapted from [13]).

of elastic grid. A new DWDM grid has been developed within the ITU-T Study Group 15 by defining a set of nominal central frequencies, channel spacing, and the concept of frequency slot. The main difference with respect to the WDM network is the way the basic unit of switching is identified which is the frequency slot now rather than a wavelength. A frequency slot is defined by its nominal central frequency in the whole spectrum range and its slot width. The set of nominal central frequencies can be built using the following expression f = 193.1 +n×0.00625 THz, where 193.1 THz is ITU-T “anchor frequency” for transmission over the C-band, and n is a positive or negative integer including 0. It means that the central frequency can be moved in the C-band at 6.25 GHz steps. The slot width determines the “amount” of optical spectrum regardless of its actual position in the spectrum. A slot width is constrained to be m×12.5GHz, where m is an integer greater than or equal to 1 and 12.5 GHz, since an even number of 6.25 GHz slots has to be allocated around the central frequency, as illustrated in Fig. 6.

Although the progress toward elastic spectrum allocation are remarkable, in order to develop truly elastic infrastructure much work on areas such as elastic transceivers, optical node design, routing and spectrum allocation algorithms, network control as well as management is still required.

2.5

Issues and Challenges in Elastic Optical Networking

Data plane architectures able to allocate spectrum flexibly are fundamental for elastic optical networks. Also, if flexible allocation is required for other kinds of network resour-ces, e.g., time and space, such functionality needs to be supported by the data plane. In addition, a desirable feature of optical nodes is to facilitate smooth hardware migration

from fixed to flex-grid. Thus, it would be possible to carry legacy signals with low cost in elastic hardware while using the more expensive elastic hardware only where required. Also, in the area of flexible transponders further developments are required. There have been several demonstrations of bitrate-variable transmitters where the number of sub-carriers or the modulation format are adapted to achieve the desired bitrate and spectral efficiency [68, 69]. However, such transceivers can generate only a single channel with a specific bitrate. Therefore, when high-speed flexible transponders operate in low speed modes, part of their transmission capacity is wasted. This has led to the idea of sliceable transceivers, which are able to slice their total capacity for transmission towards different destinations. Transceiver capacity may be sliced in one or several dimensions, e.g., frequency, time, space and polarization. However, up until now only the frequency domain has been exploited to slice a transceiver’s capacity.

3 DYNAMIC RESOURCE PROVISIONING IN

ELASTIC OPTICAL NETWORKS

Advances in physical layer technologies, as shown in Chapter 2, couple with enhanced con-trol plane solutions provide the basis to optimize the overall performance on the network level. Aspect as strategies of survivability for elastic optical networking, to enable high re-siliency against network failures, new network control and management schemes, network virtualization as well as energy efficiency strategies, which are vital to facilitate operation and maintenance of elastic optical network, need to be studied. Furthermore, efficient resource management strategies are required for the network planning and especially for dynamic spectrum allocation. In the following chapter, we discuss issues involved in the optimization of elastic optical networks, focusing most of dynamic spectrum provisio-ning, spectrum fragmentation and some elastic spectrum assignment schemes, which are common used to efficient allocate the spectral resources in EONs.

3.1

Design Scope Aspects of Networking Optimization

The emergence of elastic optical networking as a method to increase resource efficiency and provide advanced functionalities poses significant challenges on the networking level. The introduction of extra degrees of flexibility dictates the enhancement of the network planning and optimization procedure to additionally consider the manner in which these extra parameters should be set. Aspects such as network performance (examined on the connection level and on the network level), cost (consisting of capital and operational expenditures), energy efficiency, and control plane requirements are usually considered as research areas of interest, and have been attracted not only universities, but also impor-tant companies in the area of Telecommunication, e.g., Alcatel-Lucent, Fujitsu Network Communications and Huawei. Fig. 7 illustrates a categorization of different research areas with respect to elastic optical networking. Usually, one of the main parameter of interest is the performance on the network level, taking into account aspects as bit rate, transparent reach, and spectral efficiency. On the network level, on the other hand, it is important to examine the overall utilized spectrum, the blocking probability, the utilized interfaces, and the availability. In Fig. 7, a categorization of approaches for network optimization of elastic optical networks is also presented, based on the design scope, the application scope, and the selected methodology.

Figure 7: Network optimization for Elastic Optical Networks (adapted from Tomkoset al., 2014).

number of contiguous sub-carrier slots are now to be assigned. Sliceable flexible trans-ceivers can be used in principle to “relax” the spectrum contiguity constraint. However, the introduction of such devices might require a more “sophisticated” control manner of the overall network, therefore, increasing the complexity and cost. Additionally, the continuity of these sub-carrier slots should be guaranteed in a similar manner as wave-length continuity constraints are imposed. This leads to the development of routing and spectrum allocation algorithms (RSA) [15, 17, 19, 71]. Moreover, as additional degrees of freedom are allowed by elastic optical networks, new relevant constraints are required to be considered. For example as the modulation level can be selected on a connection basis, constraints tying it to the required bit rate of the traffic demand as well as to the achieved transparent reach are necessary. To this end routing, modulation level and spectrum allocation algorithms (RMLSA) have been recently proposed [14, 16]. Physical layer impairments can be considered in the planning procedure. Note that in this case the maximum transmission distance is a commonly used metric. Additionally, restrictions can be imposed on the manner in which connections are allowed to be re-routed. Re-routing may be desired for example in order to avoid blocking of new connection requests.

which achieve such defragmentation cycles can be quite expensive and even more impor-tantly, defragmentation might interfere with existing traffic. Efficient spectrum allocation schemes, discussed in the following, Subsection 3.3.1, can be used in order to minimize blocking of new connection requests in the context of spectrum fragmentation.

Another categorization involves the method used to conduct the planning. Mathe-matical optimization methods, such as integer linear programming (ILP) and Markov modeling, can be applied. Heuristic approaches can also be applied – especially if the computational complexity is a restricting factor. In this case, optimality can be sacrifi-ced in order to reduce the computation time. This leads to heuristic methods being the method of choice for dynamic planning. Note that the discussed network planning ap-proaches can be applied with different optimization objectives, such as spectrum savings and blocking performance. However, in terms of blocking performance only few works in the literature had considered Markov-based models for statistical analysis of dynamic resource provisioning in elastic optical networks and, so far, did not provide any in-depth investigation of blocking events and their relation to spectrum fragmentation as presented in this thesis.

3.2

Dynamic Resource Provisioning in EONs: Definition and

Com-plexity

There has been a considerable increase in the range of transmission rates and speed between large and small bandwidth demands that current optical networks are required to provide. Requirements for dissimilar data rates may arise from the geographic distribution of traffic or the variety of services provided. For instance, in some cases high-bit rate traffic (e.g. 100 Gb/s) may be needed for data-center interconnection, while other users may require transport connections of only 100 Mb/s, 1Gb/s and 10 Gb/s. Thus, based on this broad range of traffic granularities, it is desired that optical nodes allocate resources in a flexible and efficient manner to efficiently support high-speed channels (beyond 100G), lower speed channels (e.g. 40 Gb/s, 10Gb/s) and sub-wavelength channels (e.g. hundreds of Mb/s). The desired elastic right-size bandwidth allocation in EONs is achieved with the aid of multi-carrier solutions such as CO-OFDM technology as well as N-WDM, which have set the stage for envisioning fully elastic optical networking. As mentioned in 2.2.2, such multi-carriers solutions technologies enable the useful bandwidth of an optical fiber being discretized and divided into multiple optical frequency slots (sub-carriers). Therefore, being the width of a single optical sub-carrier can be much smaller than the width of a channel employed in a fixed-size grid scenario, such as the one defined by the ITU-T in [9]. Based on these assumptions, and considering that the bit rate requested by a connection can be converted into particular spectrum bandwidth needs, each demand

imposed by connection request can be understood as a requested numbers of frequency slots between a source and a destination node.

Elastic bandwidth provisioning enables channels to share the formerly fixed spectral resources, thus improving network efficiency. As show in Fig. 8, a portion of spectrum may be shared in the frequency domain among several services/applications that use similar or different transmission formats, e.g., number of sub-carriers, modulation format as well as bit rate. All the services/applications can coexist as long as they do not interfere with each other. In other words, for a given traffic demand, the request can be translated into a number of optical sub-carriers, and accommodated through the establishment of the corresponding spectrum path. To form the spectrum path for a connection using multiple optical sub-carriers, elastic optical networks may comprise bandwidth variable (BV) transponders at the network edge and bandwidth variable optical cross connects (OXCs) in the network core, which can be built based on the continuous bandwidth variable wavelength selective switch (WSS) [72]. Note that two spectrum paths that share one or more common fiber links, have to be separated in frequency domain to enable the optical signal filtering, i.e., two set of sub-carriers within the two spectrum paths have to be isolated by a guard frequency band (guardband). The size of the guardband, however, is not trivial and may be in the order of none, one or multiple sub-carrier(s) [73].

Figure 8: Elastic resource allocation used to carry different services/applications with custom bandwidth allocation.